Question
You are working on an Ortho-rehab unit, and investigating pain management. The nurse manager has metrics that indicate the mean patient pain score for the prior month was a 5 on a scale from 0 to 10, with 0 being no pain and 10 being the worst imaginable. The manager suggests that the standard deviation for the data is 1.5. What % of the patient population would be captured within the scale values of 5 and 9.5? ____ And how many SD units is that? ____ Between what scale values would 68% of the population likely be found? Min = ____: Max = ____ And how many SD units does that represent?____ Imagine the below results used standardized (z-scored) measures to allow comparison of various measures. At the start the researcher declared that statistical significance (alpha) would be set at p lessthanorequalto 05. The study investigated the relationship of BMI to daily grams of dietary fat consumption, number of days of exercise per week, and years of education. The following correlations with BMI were reported. Dietary Fat (r = 65, p = 04): Exercise (r = -.71, p = 01): Years of Education (r = 09, p = 62). Which of the three measures are significantly related to BMI? Which measure seems to have the strongest impact on BMI? Write a sentence that describes the relationship between BMI and Exercise. Significance & statistical error: In the above study, the researcher set p lessthanorequalto 05 as the level of significance. Some things can never be truly 'known' but assume that the results are valid and a reflection of the truth. Assuming all other things stayed the same, imagine if instead the researcher had declared p lessthanorequalto 01 as the criteria for statistical significance at the start of the study. What would be the implication for Diet in their study? Under the assumption that the above original results were 'correct', what type of error has now occurred? What does this type of error imply or mean?
Explanation / Answer
2.) (i) Let x denote the score
mean = = 5, standard deviation = sd= = 1.5
Percentage required= P(x>0.5) - P(x>9.5)
Using normal distribution approximation
we get, = P(Z> (0.5-5)/1.5) - P(Z>(9.5-5)/1.5)
= P(Z> -3) - P(Z>3) = P(Z<3) - { 1-P(Z<3)} = 2*P(Z<3) - 1= 2*0.99865 -1= 0.9973
So, 99.73% of the patient population would be captured in 0.5 to 9.5 scale
2.) (ii) It is '+-3' standard deviation units or within 3 standard deviations of mean
2.) (iii) In a standard normal distribution 68% of the values lie within 1 standard deviation of the mean
so, as z = (x-mean)/sd so, x = (z*sd) + mean
so, as z= +1 so, x=(1*1.5)+5 = 6.5
and as z=-1 so, x= (-1*1.5)+5 = 3.5
hence, 68% of the values would be found between min=3.5, max= 6.5
2.) (iv) It is '+-1' standard deviation units or within 1 standard deviations of mean
